Evolution of the reflection and focusing patterns and stress states in two-fluid cylindrical shell systems subjected to an external shock wave

Several most important features of the hydrodynamic field induced inside a circular cylindrical shell filled with and submerged into different fluids when it is subjected to an external shock wave are considered. This investigation is a follow-up of an earlier study of the two-fluid shell-shock interaction [S. Iakovlev, Interaction between an external shock wave and a cylindrical shell filled with and submerged into different fluids, Journal of Sound and Vibration 322 (2009) 401-437], and it addresses a number of practically important issues not covered in that work. The focus of this study is on the evolution of the respective hydrodynamic patterns in response to the continuous change of the parameters of the fluids, in particular the speed of sound. Along with the analysis of the hydrodynamic patterns it is also demonstrated that when one is concerned with the highest pressure attained inside the shell, the most dangerous combination of the parameters occurs when the ratio of the internal and external acoustic speeds is close to 0.48, with the respective pressure exceeding the maximum incident pressure by more than 110 percent. The effect that the hydrodynamic features discussed have on the stress state of the shell is addressed as well, and it is observed that the maximum tensile stress is significantly affected by the evolution of the considered hydrodynamic features, whereas the maximum compressive stress is not. It is also observed that the maximum tensile stress is very sensitive to the change of the ratio of the acoustic speeds in the internal and external fluids, with as little an increase of the latter as 13 percent resulting in more than doubling of the former in some cases.     

INTERACTION OF A SPHERICAL SHOCK WAVE AND A SUBMERGED FLUID-FILLED CIRCULAR CYLINDRICAL SHELL

The complete three-dimensional interaction between a spherical shock wave and a submerged fluid-filled elastic circular cylindrical shell is considered. A hybrid analytical-numerical solving procedure is established. An exact analytical solution in the form of double Fourier series with time-depending coefficients is obtained for the hydrodynamic pressure. Displacements of a shell are approached analytically to reduce the problem to a set of systems of ordinary differential equations, which are treated numerically. Detailed analysis of the interaction is performed with emphasis given to the stress-strain state. A few important features of the interaction process have been found. In particular, it has been shown that the interior fluid not only substantially affects the magnitude of displacements and stresses, but also dramatically changes the nature of the interaction. It has been found that the absolute maximum of stresses can neither be caused by a direct action of a shock wave nor by a constructive superpose of elastic waves in the shell, but by the pressure wave propagating in the interior fluid. This fact seems to be of essential importance for engineering applications, especially when safety is a primary design concern. Another important result is that the maximum stresses are attained at large times, which makes use of early time asymptotics leading to incorrect results. The proposed semi-analytical approach seems to be computationally attractive and suitable for extensive numerical simulations.     

Free vibration analysis of a hanged clamped-free cylindrical shell partially submerged in fluid: The effect of external wall,internal shaft,and flat bottom

The free flexural vibration of a hanged clamped-free cylindrical shell with various boundary conditions partially submerged in a fluid is investigated. Specifically, the effects of the boundary conditions such as the existence of the external wall, internal shaft, and bottom on the natural vibration characteristics of the partially submerged cylindrical shell are investigated both theoretically and experimentally. The fluid is assumed to be inviscid and irrotational. The cylindrical shell is modeled by using the Rayleigh–Ritz method based on the Sanders shell theory. The kinetic energy of the fluid is derived by solving a boundary-value problem related to the fluid motion. The theoretical predictions were in good agreement with the experimental results validating the theoretical approach developed in this study. The effects of the external wall, internal shaft, and bottom on the natural vibration characteristics can be neglected when its boundaries are not very close to the shell structure.     

Circumferential waves for a cylindrical shell in smooth contact with a continuum

Dispersion relations are determined for circumferential waves propagating in a layered, circular cylinder by using shell equations to approximate the behavior of the outer layer. These equations include the effects of transverse shear deformation and rotatory inertia. The cylinder consists of an elastic core in smooth contact with a hollow, circular cylinder of distinctly different elastic properties. Two distinct modes exist as the shell thickness reduces to zero. One mode is recognized to be surface waves on the convex cylindrical surface of the core; the second mode is associated with long longitudinal waves in the shell. The approximate dispersion curves for these modes are compared with curves obtained by employing elasticity equations for the layer. As the curvature increases, the agreement of the two theories becomes progressively poorer whether or not any disagreement exists for the case of no curvature. The agreement of the two theories is better when the layer is relatively stiff than when the layer is relatively soft. The shell equations simplify the calculations necessary to produce the dispersion curves.     

Acoustic signature of a submarine hull under harmonic excitation

The structural and acoustic responses of a submarine under harmonic force excitation are presented. The submarine hull is modelled as a cylindrical shell with internal bulkheads and ring stiffeners. The cylindrical shell is closed by truncated conical shells, which in turn are closed at each end using circular plates. The entire structure is submerged in a heavy fluid medium. The structural responses of the submerged vessel are calculated by solving the cylindrical shell equations of motion using a wave approach and the conical shell equations with a power series solution. The far-field radiated sound pressure is then calculated by means of the Helmholtz integral. The contribution of the conical end closures on the radiated sound pressure for the lowest circumferential mode numbers is clearly observed. Results from the analytical model are compared with computational results from a fully coupled finite element/boundary element model.     

Acoustic wave in a suspension of magnetic nanoparticle with sodium oleate coating

The ultrasonic propagation in the water-based magnetic fluid with doubled layered surfactant shell was studied. The measurements were carried out both in the presence as well as in the absence of the external magnetic field. The thickness of the surfactant shell was evaluated by comparing the mean size of magnetic grain extracted from magnetization curve with the mean hydrodynamic diameter obtained from differential centrifugal sedimentation method. The thickness of surfactant shell was used to estimate volume fraction of the particle aggregates consisted of magnetite grain and surfactant layer. From the ultrasonic velocity measurements in the absence of the applied magnetic field, the adiabatic compressibility of the particle aggregates was determined. In the external magnetic field, the magnetic fluid studied in this article becomes acoustically anisotropic, i.e., velocity and attenuation of the ultrasonic wave depend on the angle between the wave vector and the direction of the magnetic field. The results of the ultrasonic measurements in the external magnetic field were compared with the hydrodynamic theory of Ovchinnikov and Sokolov (velocity) and with the internal chain dynamics model of Shliomis, Mond and Morozov (attenuation).     

充水有限长圆柱薄壳声散射:Ⅰ.理论

研究水中充水有限长圆柱薄壳的声散射。采用弹性薄壳理论结合边界条件导出了有限长圆柱薄壳倾斜入射时散射声场的解析解,内部充水的作用反映在系统总阻抗中增加了内部流体阻抗。数值计算表明,在反向散射声场中,刚性散射部分仅在正横附近有比较大的贡献,而斜入射时起主要作用的是弹性散射部分。散射波相速度频散曲线的计算表明,与内部真空的情况相比内部充水后除正横附近的纵波和剪切波以外,增加了一组内部流体引起的附加波,其对散射声场贡献非常重要。在计算的频率-角度谱图中,内部流体附加波呈现"碗"形共振曲线。      

Breakdown of hydrodynamics in a simple one-dimensional fluid

We investigate the behavior of a one-dimensional diatomic fluid under a shock wave excitation. We find that the properties of the resulting shock wave are in striking contrast with those predicted by hydrodynamic and kinetic approaches; e.g., the hydrodynamic profiles relax algebraically toward their equilibrium values. Deviations from local thermodynamic equilibrium are persistent, decaying as a power law of the distance to the shock layer. Nonequipartition is observed infinitely far from the shock wave, and the velocity-distribution moments exhibit multiscaling. These results question the validity of simple hydrodynamic theories to understand collective behavior in 1D fluids.     

ICF流体力学不稳定性实验用柱状激波管的研制

在惯性约束聚变(ICF)实验中,点火靶丸表面(界面)的粗糙度和缺陷所产生的流体力学不稳定性是决定点火成功与否的关键因素之一,设计和研制流体力学不稳定性分解实验用靶是解决该问题的主要技术手段。结合国内外的研究现状和神光-Ⅱ激光装置的特点,设计并研制了一种新型柱状激波管。该靶型由三种介质组成,分别为调制聚苯乙烯(CH)圆片、柱状碳气凝胶(CRF)和CH微套管。调制CH圆片和柱状CRF通过微加工技术装配到CH微套管内,封装后形成柱状激波管。介绍了该靶型的设计原理和详细的制备工艺,并对相应的靶参数进行了测量。结果表明:柱状CRF气凝胶具有较好的成型性,长度、直径和密度分别为1000μm、730μm和250mg·cm-3;CH圆片的厚度和直径分别为15μm和730μm,表面调制图形的周期和峰谷差分别为100μm和4.3μm;实验得到的柱状激波管的轴向和径向最大装配误差分别为2μm和3μm。     

准周期加隔板有限长圆柱壳声散射

研究准周期加隔板有限长圆柱壳在水中的声散射特性,隔板位置存在小的随机偏差.首先给出理论推导,通过计算周期加隔板情况验证理论公式的正确性.然后以角度-频率谱形式给出准周期加隔板圆柱壳声散射计算结果.计算表明隔板的准周期性导致Bloch-Floquet弯曲波和散射声场背景出现扩散和增强现象,而近乎平行于横轴的由隔板共振引起的亮条纹被散射声场背景所掩盖.最后讨论了随机因子、隔板个数以及隔板间距对Bragg散射的影响.计算表明随机因子越大Bragg散射条纹的频率范围越宽扩散越明显,隔板个数越多Bragg散射条纹的频率范围越窄能量越集中,隔板间距变大时Bragg散射条纹增多而且越高阶次的Bragg散射条纹扩散越严重.根据Bragg散射的几何特征导出的近似估算公式可以较准确预报Bragg散射在频谱图上的位置,也可以大致预报隔板准周期排列时Bragg散射的扩散现象.     

Resonant acoustic scattering by a finite linear grating of elastic shells

Theoretical and experimental studies of the acoustic scattering by a finite linear grating of elastic cylindrical shells are performed. It is observed that a resonant interaction takes place at low frequency when the shells are very close to each other. This phenomenon can be clearly associated to the Scholte-Stoneley wave that propagates around a single shell. It is shown that each resonance of the Scholte-Stoneley wave is split up into N resonances when N shells compose the grating.     

Application of the wavenumber jump condition to the normal and oblique interaction of a plane acoustic wave and a plane shock

A kinematic approach is considered whereby the wavenumber jump conditions in conjunction with the appropriate dispersion relations is applied to the investigation of the normal and oblique interaction of a plane acoustic wave with a plane shock wave. For the normal interaction of an acoustic wave with a stationary plane shock a logarithmic shift in the wave spectra is obtained. For the normal interaction with a moving shock front it is shown that for shock Mach numbers above a critical value, the frequency of the transmitted wave becomes negative. This results in the fact that the crests of the transmitted signal arrive at a fixed observer in a reverse order to their generation. Finally, the oblique interaction of an acoustic wave with a stationary shock is considered. The “Snell's Law” for the transmitted wave is derived and two special angles of incidence are identified. The first is a no-refraction angle: i.e., the transmitted wave angle is the same as the incident wave angle. The second is a critical angle such that for incident angles greater than this critical angle there is no transmitted wave. A necessary and sufficient condition for the existence of a transmitted wave is derived in terms of the speed of sound and Mach number of the fluid and the frequency and tangential wavenumber component of the incident wave.The dynamics aspects of the interaction concerning the determination of the frequency independent transmission coefficients and shock displacements are determined for the simple case of the normal interaction with a moving shock as an illustration.     

Unsteady fluid dynamic forces on a simply-supported circular cylinder of finite length conveying a flow,with applications to stability analysis

An exact analytic expression for the unsteady fluid pressure acting on the internal walls of a simply-supported circular cylindrical tube of finite length, carrying flow, is presented. The generalized force coefficients corresponding to specific modes of deformation are given explicitly. The results are applied to two problems: (1) the interaction of flow and buckling of thin-walled cylindrical shells subjected to lateral pressure and/or end thrust; (2) the aeroelastic stability of the shells. The second problem is aimed at resolving some controversy about post-divergence flutter oscillation of cylindrical shells or plates exposed to a subsonic flow. The shell equation, of the Morley type, is solved by Galerkin's method and an analytic approach is used to examine the stability of the system. It is important that damping be taken into account in the analysis. The undeformed configuration is always unstable when the flow speed exceeds the minimum divergence boundary.     

Leaky helical flexural wave backscattering contributions from tilted water-filled cylindrical shells

Helical flexural waves on a bluntly truncated tilted water-filled cylindrical steel shell in water are found to give large contributions to the backscattering above the coincidence frequency. The presence of the water inside the shell increases the damping of the leaky wave when short tone bursts are used. The magnitude of the scattering is found by modifying a ray analysis developed for empty shells. When longer bursts are used, some of the internally radiated energy (corresponding to the case of one internal chord) is superposed on the ordinary helical ray backscattering. This occurs as a consequence of the internal excitation of helical rays.     

Acoustic radiation from a shell-encapsulated baffled cylindrical cap

An exact study of radiation of an acoustic field due to radial/axial vibrations of a baffled cylindrical piston, eccentrically positioned within a fluid-filled thin cylindrical elastic shell, into an external fluid medium is presented. This configuration, which is a realistic idealization of a liquid-filled cylindrical acoustic lens with a focal point inside the lens when used as a sound projector, is of practical importance with a multitude of possible applications in underwater acoustics and ocean engineering. The formulation utilizes the appropriate wave field expansions along with the translational addition theorems for cylindrical wave functions to develop a closed-form solution in the form of an infinite series. Numerical results reveal the key effects of excitation frequency, cap angle, radiator position (eccentricity), dynamics of the elastic shell, and cap surface velocity distribution on sound radiation.     

Absorption of electromagnetic radiation by a bimetallic cylindrical particle of finite length

The absorption cross section of electromagnetic radiation is calculated for a bimetallic cylindrical particle of finite length. A general case is considered, where the ratio of the radius of the particle core to the particle radius and the ratio of the radius of the particle to its length can take arbitrary values. The conditions of diffuse reflection of electrons from the internal and external surfaces of the metal shell of the particle and from its faces are used as the boundary conditions of the problem. The effect of the ratio of the radius of the core of a bimetallic cylindrical particle to the particle radius and the ratio of the radius of the particle to its length on the electromagnetic properties of the particle is analyzed.     

Acoustic scattering characteristics of a thick-walled orthotropic cylindrical shell at oblique incidence

The method of wave function expansion is adopted to study the scattering of a plane harmonic acoustic wave incident at an arbitrary angle upon an arbitrarily thick cylindrically orthotropic homogeneous cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the three-dimensional exact equations of anisotropic elasticity. The solution is used to correlate the perturbation in the material elastic constants of an air-filled and water-submerged aluminium cylindrical shell to the sensitivity of resonances associated with various modes of wave propagation appearing in the backscattered amplitude spectrum (i.e., axially guided, Lamb, Rayleigh and Whispering Gallery waves). The effects of shell wall thickness as well as inner fluid loading on the frequency response of the shell are also examined. A limiting case is considered and good agreement with the solution available in the literature is obtained.     

Acoustic scattering from a fluid-filled finite cylindrical shell in water:Ⅰ.Theory

Acoustic scattering from a submerged fluid-filled finite cylindrical shell insonified by an incident plane wave was studied.The analytic solutions of the scattering field are derived using the elastic thin shell theory with the boundary conditions.The fluid-filled impedance,due to the effect of internal fluid,must add to the impedance of the system.The results show that in the backscattering field,rigid scattering has a large contribution only on the broadside and elastic scattering play a major role when oblique incidence.The dispersion curves of the phase velocity show that comparing with the internal vacuum condition,except the contribution by longitudinal wave and shear wave near the broadside a series of the additional waves caused by the internal fluid is added which have great contribution to the scattering field.Bowl-shape resonance curves are presented in the frequency-angle spectrum as the contribution of the internal fluid waves.     

Experimental investigation of the generation of large-amplitude internal solitary wave and its interaction with a submerged slender body

A principle of generating the nonlinear large-amplitude internal wave in a stratified fluid tank with large cross-section is proposed according to the‘jalousie’control mode.A new wave-maker based on the principle was manufactured and the experiments on the generation and evolution of internal solitary wave were conducted.Both the validity of the new device and applicability range of the KdV-type internal soliton theory were tested.Furthermore,a measurement technique of hydrodynamic load of internal waves was developed.By means of accurately measuring slight variations of internal wave forces exerted on a slender body in the tank,their interaction characteristics were determined.It is shown that through establishing the similarity between the model scale in the stratified fluid tank and the full scale in the numerical simulation the obtained measurement results of internal wave forces are confirmed to be correct.     

Axially symmetric vibrations of fluid-filled poroelastic circular cylindrical shells

Employing Biot's theory of wave propagation in liquid saturated porous media, axially symmetric vibrations of fluid-filled and empty poroelastic circular cylindrical shells of infinite extent are investigated for different wall-thicknesses. Let the poroelastic cylindrical shells are homogeneous and isotropic. The frequency equation of axially symmetric vibrations each for a pervious and an impervious surface is derived. Particular cases when the fluid is absent are considered both for pervious and impervious surfaces. The frequency equation of axially symmetric vibrations propagating in a fluid-filled and an empty poroelastic bore, each for a pervious and an impervious surface is derived as a limiting case when ratio of thickness to inner radius tends to infinity as the outer radius tends to infinity. Cut-off frequencies when the wavenumber is zero are obtained for fluid-filled and empty poroelastic cylindrical shells both for pervious and impervious surfaces. When the wavenumber is zero, the frequency equation of axially symmetric shear vibrations is independent of nature of surface, i.e., pervious or impervious and also it is independent of presence of fluid in the poroelastic cylindrical shell. Non-dimensional phase velocity for propagating modes is computed as a function of ratio of thickness to wavelength in absence of dissipation. These results are presented graphically for two types of poroelastic materials and then discussed. In general, the phase velocity of an empty poroelastic cylindrical shell is higher than that of a fluid-filled poroelastic cylindrical shell.The phase velocity of a fluid-filled bore is higher than that of an empty poroelastic bore. Previous results are shown as a special case of present investigation. Results of purely elastic solid are obtained.